{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Random Forest Regression\n",
    "\n",
    "A [random forest](https://en.wikipedia.org/wiki/Random_forest) is a meta estimator that fits a number of classifying [decision trees](https://en.wikipedia.org/wiki/Decision_tree_learning) on various sub-samples of the dataset and use averaging to improve the predictive accuracy and control over-fitting. The sub-sample size is always the same as the original input sample size but the samples are drawn with replacement (can be changed by user).\n",
    "\n",
    "Generally, Decision Tree and Random Forest models are used for classification task. However, the idea of Random Forest as a regularizing meta-estimator over single decision tree is best demonstrated by applying them to regresion problems. This way it can be shown that, **in the presence of random noise, single decision tree is prone to overfitting and learn spurious correlations while a properly constructed Random Forest model is more immune to such overfitting.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create some syntehtic data using scikit-learn's built-in regression generator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 543,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 544,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import make_regression method to generate artificial data samples \n",
    "from sklearn.datasets import make_regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What is *make_regression* method?\n",
    "\n",
    "It is a convinient method/function from scikit-learn stable to generate a random regression problem. The input set can either be well conditioned (by default) or have a low rank-fat tail singular profile.\n",
    "\n",
    "The output is generated by applying a (potentially biased) random linear regression model with `n_informative` nonzero regressors to the previously generated input and some gaussian centered noise with some adjustable scale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 545,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_samples = 100 # Number of samples\n",
    "n_features = 6 # Number of features\n",
    "n_informative = 3 # Number of informative features i.e. actual features which influence the output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 546,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y,coef = make_regression(n_samples=n_samples, n_features=n_features, n_informative=n_informative,\n",
    "                       random_state=None, shuffle=False,noise=20,coef=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Make a data frame and create basic visualizations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Data Frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 547,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th>X4</th>\n",
       "      <th>X5</th>\n",
       "      <th>X6</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.126157</td>\n",
       "      <td>1.537836</td>\n",
       "      <td>0.806673</td>\n",
       "      <td>-1.491675</td>\n",
       "      <td>0.299527</td>\n",
       "      <td>-1.474775</td>\n",
       "      <td>163.192326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.069024</td>\n",
       "      <td>0.054889</td>\n",
       "      <td>1.039015</td>\n",
       "      <td>-1.735270</td>\n",
       "      <td>1.821929</td>\n",
       "      <td>-1.468514</td>\n",
       "      <td>27.475965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.768465</td>\n",
       "      <td>0.987083</td>\n",
       "      <td>1.031437</td>\n",
       "      <td>0.188459</td>\n",
       "      <td>0.777789</td>\n",
       "      <td>0.479504</td>\n",
       "      <td>119.033181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.656240</td>\n",
       "      <td>1.082382</td>\n",
       "      <td>-1.189696</td>\n",
       "      <td>0.407922</td>\n",
       "      <td>-0.365730</td>\n",
       "      <td>0.229083</td>\n",
       "      <td>-40.529855</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.014315</td>\n",
       "      <td>-0.393556</td>\n",
       "      <td>0.957417</td>\n",
       "      <td>-0.281082</td>\n",
       "      <td>1.336032</td>\n",
       "      <td>-1.126818</td>\n",
       "      <td>51.106814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.573993</td>\n",
       "      <td>-0.325107</td>\n",
       "      <td>1.364623</td>\n",
       "      <td>-0.250283</td>\n",
       "      <td>-0.188160</td>\n",
       "      <td>-1.172770</td>\n",
       "      <td>79.695119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.157546</td>\n",
       "      <td>-1.190279</td>\n",
       "      <td>-1.062111</td>\n",
       "      <td>0.967536</td>\n",
       "      <td>-0.412225</td>\n",
       "      <td>1.300293</td>\n",
       "      <td>-152.172329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.401044</td>\n",
       "      <td>-0.327829</td>\n",
       "      <td>1.166431</td>\n",
       "      <td>1.737604</td>\n",
       "      <td>-1.131857</td>\n",
       "      <td>1.081729</td>\n",
       "      <td>83.956168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.357468</td>\n",
       "      <td>1.440760</td>\n",
       "      <td>-0.421540</td>\n",
       "      <td>-0.379527</td>\n",
       "      <td>0.317447</td>\n",
       "      <td>0.841242</td>\n",
       "      <td>118.143163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-1.690400</td>\n",
       "      <td>-0.298059</td>\n",
       "      <td>1.984504</td>\n",
       "      <td>-0.578445</td>\n",
       "      <td>-0.115120</td>\n",
       "      <td>-1.034285</td>\n",
       "      <td>32.072988</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         X1        X2        X3        X4        X5        X6           y\n",
       "0  0.126157  1.537836  0.806673 -1.491675  0.299527 -1.474775  163.192326\n",
       "1 -1.069024  0.054889  1.039015 -1.735270  1.821929 -1.468514   27.475965\n",
       "2 -0.768465  0.987083  1.031437  0.188459  0.777789  0.479504  119.033181\n",
       "3 -0.656240  1.082382 -1.189696  0.407922 -0.365730  0.229083  -40.529855\n",
       "4 -0.014315 -0.393556  0.957417 -0.281082  1.336032 -1.126818   51.106814\n",
       "5 -0.573993 -0.325107  1.364623 -0.250283 -0.188160 -1.172770   79.695119\n",
       "6  0.157546 -1.190279 -1.062111  0.967536 -0.412225  1.300293 -152.172329\n",
       "7  0.401044 -0.327829  1.166431  1.737604 -1.131857  1.081729   83.956168\n",
       "8  1.357468  1.440760 -0.421540 -0.379527  0.317447  0.841242  118.143163\n",
       "9 -1.690400 -0.298059  1.984504 -0.578445 -0.115120 -1.034285   32.072988"
      ]
     },
     "execution_count": 547,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame(data=X,columns=['X'+str(i) for i in range(1,n_features+1)])\n",
    "df2=pd.DataFrame(data=y,columns=['y'])\n",
    "df=pd.concat([df1,df2],axis=1)\n",
    "df.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Scatter plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 548,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TtPZJfW/ikqShuz7vp3H8+HHuvPNOtm/fHu02RY1l9tPogdUXCYUraufb15pD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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d130a6a080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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fpm/fM1s1nz4j/Kc//SlTpkyJfilDJD2NzjWvh759G2m//EWbdQlgkU/jncg+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\nVsC3rcWYMWNavH7cuHFMmzaN6667jl6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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d12f7220f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2CL/jjjuYOnVq9EsZprhfEd6FnD4qnv83L7RcT5EUwsrvYHQWAHE1o7ib8Zw/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\nf8LAOmjZpFDvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d12f7bd3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Evn8fqTVn/P3WrafQAZCagXq8ivO7PtLV1WCV/EZSIuRZfWiZv8vm2wrsdhVP2+yppcvw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\nCCF0+/8EU9M3nzo90wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d130fc82e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dPdUqGP9UG8ywkHryBLjcWPZ9Drru3YjXTDlTQ+rGdZ3OQ5ih/AEH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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d12eefd6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RucjFyow6k61FCqeQWhod7RF+8cUX88ILL0SscL0lLQ2dnL/wnTxO4u/eREtP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\n3kHA7eMLwMsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d12f0c0908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with plt.style.context(('seaborn-dark')):\n",
    "    for i,col in enumerate(df.columns[:-1]):\n",
    "        plt.figure(figsize=(6,4))\n",
    "        plt.grid(True)\n",
    "        plt.xlabel('Feature:'+col,fontsize=12)\n",
    "        plt.ylabel('Output: y',fontsize=12)\n",
    "        plt.scatter(df[col],df['y'],c='red',s=50,alpha=0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### It is clear from the scatter plots that some of the features influence the output while the others don't. This is the result of choosing a particular *n_informative* in the *make_regression* method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Histograms of the feature space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 549,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d12ef0d8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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f99SnTx/5+vpq2bJlqqqq0rVr13T8+PF6C+yTTz7Rrl27NH/+fEnSokWLtGXL\nFu3Zs0fSz5/JxcbG6g9/+INeeOGF5v71AE5BYQFNEBwcrPfee09Lly5VRESEoqKitGLFCtXU1Khd\nu3ZauHChnn/+eYWFhenDDz/UyJEjbet269ZNY8eOVe/evRUaGqqSkhIlJSXpgQceUM+ePZWQkHDT\nNVM3atOmjbKzs3X06FH16tVL9913n6ZPn65Lly5J+vmkiV/OAKysrNSrr76qhQsX2p6uHBgYqHnz\n5ik1NVVVVVX65z//qRMnTmjBggV1rjcDjIQHOAIATIEjLACAKVBYAABToLAAAKZAYQEATIHCAgCY\nAoUFADAFCgsAYAoUFgDAFCgsAIAp/B/cJrs6r4HoIAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d12eac0a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BrK2tIZPJ0L17dyxcuLDZtxM8LqlUCgAoKytTaS8rK4OdnV2z4+zs7JocY2ZmBhsbG63U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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d12f2edcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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tsx4BWFtbq+eee04ZGRnWux4HBgZqyZIlSk5OVn19vW699VYFBQVZHx06dJDF\nYrH7TrCAM3ADRwCAEdjDAgAYgcICABiBwgIAGIHCAgAYgcICABiBwgIAGIHCAgAYgcICABiBwgIA\nGOH/APuGTM4SmlMPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d12f7af898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d12f713908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3bli4cGGzTydoKalUCgAoKytTWV9WVgY7O7tm+9nZ2TXZx8zMDDY2NlqpjYiIjJfGH1em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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d130ad97b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with plt.style.context(('fivethirtyeight')):\n",
    "    for i,col in enumerate(df.columns[:-1]):\n",
    "        plt.figure(figsize=(6,4))\n",
    "        plt.grid(True)\n",
    "        plt.xlabel('Feature:'+col,fontsize=12)\n",
    "        plt.ylabel('Output: y',fontsize=12)\n",
    "        plt.hist(df[col],alpha=0.6,facecolor='g')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How will a Decision Tree regressor do?\n",
    "\n",
    "Every run will generate different result but on most occassions, **the single decision tree regressor is likely to learn spurious features** i.e. will assign small importance to features which are not true regressors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 550,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 551,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeRegressor(criterion='mse', max_depth=5, max_features=None,\n",
       "           max_leaf_nodes=None, min_impurity_decrease=0.0,\n",
       "           min_impurity_split=None, min_samples_leaf=1,\n",
       "           min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "           presort=False, random_state=None, splitter='best')"
      ]
     },
     "execution_count": 551,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_model = tree.DecisionTreeRegressor(max_depth=5,random_state=None)\n",
    "tree_model.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 566,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative importance of the features:  [ 0.06896493  0.35741588  0.54578154  0.0230699   0.          0.00476775]\n"
     ]
    },
    {
     "data": {
      "image/png": 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3liTt2rVLkyZNss2/6667FBAQoHfeeaf0qrxJI0aMUIcOHTRmzBhJUmpq6nUf3qldu7b+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\n7p6fOnXqKDAw0Bb+8tugQYMK3AuZz83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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d13085f080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Relative importance of the features: \",tree_model.feature_importances_)\n",
    "with plt.style.context('dark_background'):\n",
    "    plt.figure(figsize=(10,7))\n",
    "    plt.grid(True)\n",
    "    plt.yticks(range(n_features+1,1,-1),df.columns[:-1],fontsize=20)\n",
    "    plt.xlabel(\"Relative (normalized) importance of parameters\",fontsize=15)\n",
    "    plt.ylabel(\"Features\\n\",fontsize=20)\n",
    "    plt.barh(range(n_features+1,1,-1),width=tree_model.feature_importances_,height=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Print the $R^2$ score of the Decision Tree regression model\n",
    "\n",
    "Even though the $R^2$ score is pretty high, the model is slightly flawed because it has assigned importance to regressors which have no true significance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 553,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Regression coefficient: 0.95695111153\n"
     ]
    }
   ],
   "source": [
    "print(\"Regression coefficient:\",tree_model.score(X,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Forest Regressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 554,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.ensemble import RandomForestRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 555,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestRegressor(bootstrap=True, criterion='mse', max_depth=5,\n",
       "           max_features='auto', max_leaf_nodes=5,\n",
       "           min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "           min_samples_leaf=1, min_samples_split=2,\n",
       "           min_weight_fraction_leaf=0.0, n_estimators=100, n_jobs=1,\n",
       "           oob_score=False, random_state=None, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 555,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = RandomForestRegressor(max_depth=5, random_state=None,max_features='auto',max_leaf_nodes=5,n_estimators=100)\n",
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Print the relative importance of the features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 565,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative importance of the features:  [ 0.03456204  0.46959355  0.49500136  0.          0.          0.00084305]\n"
     ]
    },
    {
     "data": {
      "image/png": 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HAABA+WYpONpsttKuAwAAAOUcN8cAAADAEoIjAAAALCE4AgAAwBKCIwAAACwh\nOAIAAMASgiMAAAAsITgCAADAEoIjAAAALCE4AgAAwBKCIwAAACwhOAIAAMASgiMAAAAsITgCAADA\nEoIjAAAALCE4AgAAwBKCIwAAACwhOAIAAMASgiMAAAAsITgCAADAEoIjAAAALCE4AgAAwBKCIwAA\nACwhOAIAAMASgiMAAAAsITgCAADAEoIjAAAALCE4AgAAwBKCIwAAACwhOAIAAMASgiMAAAAsITgC\nAADAEoIjAAAALCE4AgAAwBKCIwAAACwhOAIAAMASgiMAAAAsITgCAADAEoIjAAAALCE4AgAAwBKC\nIwAAACwhOAIAAMASgiMAAAAsqbDBsX///jLGKDY29qpzlixZImOMBg4cKElq1KiRjDFXHXPnzi2r\n8gEAAMqdys4uoLRERUXp2WefVdeuXTVo0CD95z//cXh+wIABCg4OVmxsrKZNm+bw3LZt27Rw4cIC\n29y5c2ep1gwAAFCeVdjgKElhYWFq1aqVJkyYoJUrV+qXX36RJPn6+mrSpEnKyMhQ//79C6y3bds2\nvf3222VdLgAAQLlWYd+qlqT09HSFhYXJw8NDMTExstlsstlsiomJkYeHh8LDw5WWlubsMgEAAFxC\nhT7jKEmLFy9WZGSkQkNDNXr0aElSQECAoqOjtWDBgkLXuf322xUeHq7atWvr+PHj2rhxo3bs2FGW\nZQMAAJQ7FT44StLQoUPVrl07jRgxQpKUlJSkIUOGXHX+008/raefftphWVxcnPr166eUlJRSrRUA\nAKC8cpNknF1EWejXr59mzZolSerUqZOWL19eYE7dunX117/+VQsXLtTBgwclSQ8++KDGjh2r9u3b\n69dff9VDDz2ks2fPFvoaYWFhCg8PlyQ1b95cCQkJpbMzKFF+fn7as2ePs8uABfTKtdAv10GvXEdp\n9qpFixaW5pmKPtzd3c3u3btNvpkzZxZpfZvNZjZu3GiMMWbIkCGW1snOznb6fjOsjfj4eKfXwKBX\nFXHQL9cZ9Mp1Rmn1yup2K/TNMfkmTJggPz8/TZ48WQkJCQoNDVWXLl0sr3/x4kXNnDlTkvTEE0+U\nVpkAAADlWoUPjoGBgRo8eLASExM1fPhw9e3bVzk5OZoxY4Zq165teTvp6emSJA8Pj9IqFQAAoFyr\n0MHR09NT0dHRys3NVUhIiC5cuKBdu3Zp1KhR8vLyKvDB39fy6KOPSpL92kcAAICbTYUOjtOnT5e3\nt7dGjhylf9n4AAAgAElEQVTp8HE6ERERWrdunXr06KE+ffrYlzdv3lxubm4FttO+fXsNGzZMkhQT\nE1P6hQMAAJRDFfbjeEJCQtSzZ0+tXbtWERERDs8ZY9SvXz8lJiZq6tSpWrNmjVJTU/XRRx/J19dX\nGzZs0KFDhyT9cVd1hw4dJEkjR47Uxo0by3xfAAAAyoMKecbRx8dHU6dOVWZmpl588UUZYwrMSU5O\n1rBhw+Tp6amoqChJ0ueff66EhAS1aNFCYWFhGjRokHx9ffXFF1/o8ccf17vvvlvWuwIAAFBuVMgz\njikpKfL09LzuvMjISEVGRtofR0VF2UMkAAAAHFXIM44AAAAoeQRHAAAAWEJwBAAAgCUERwAAAFhC\ncAQAAIAlBEcAAABYQnAEAACAJQRHAAAAWEJwBAAAgCUERwAAAFhCcAQAAIAlBEcAAABYQnAEAACA\nJQRHAAAAWEJwBAAAgCUERwAAAFhCcAQAAIAlBEcAAABYQnAEAACAJQRHAAAAWEJwBAAAgCUERwAA\nAFhCcAQAAIAlBEcAAABYQnAEAACAJQRHAAAAWEJwBAAAgCUERwAAAFhCcAQAAIAlBEcAAABYQnAE\nAACAJQRHAAAAWEJwBAAAgCUERwAAAFhCcAQAAIAlBEcAAABYQnAEAACAJQRHAAAAWEJwLCVVq7k7\nuwQAAIASRXAEAACAJQRHAAAAWEJwBAAAgCUERwAAAFhCcAQAAIAlBEcAAABYQnAEAACAJQRHAAAA\nWEJwBAAAgCUVNjj2799fxhjFxsZedc6SJUtkjNHAgQMdlleqVEmhoaFau3atTpw4obNnz+rAgQOa\nN2+efH19S7t0AACAcqnCBseoqCgtWrRIQUFBGjRoUIHnBwwYoODgYMXGxmratGn25R4eHlqxYoVm\nzpypGjVqaPbs2ZoyZYrWr1+vli1bqmnTpmW5GwAAAOWKqaijbt26Ji0tzWRnZ5umTZval/v6+prs\n7GyTnp5u6tev77BOTEyMMcaY8PDwQrdZuXJlS6994WKe0/efYW3Ex8c7vQYGvaqIg365zqBXrjNK\nq1dWt1thzzhKUnp6usLCwuTh4aGYmBjZbDbZbDbFxMTIw8ND4eHhSktLs89v3ry5+vTpo3nz5unT\nTz8tdJt5eXllVT4AAEC5UtnZBZS2xYsXKzIyUqGhoRo9erQkKSAgQNHR0VqwYIHD3BdeeEGSNHfu\nXNWsWVPPPPOMfHx8dPz4ca1evVoHDhwo8/oBAADKiwofHCVp6NChateunUaMGCFJSkpK0pAhQwrM\na9GihSSpUaNGOnDggOrUqWN/7tKlS5o2bZqGDBmiS5culU3hAAAA5chNERyzs7M1btw4zZo1S5I0\ncOBAZWdnF5hXr149SdJHH32khQsXauTIkTp06JBatmyp6dOna/DgwUpPT9fbb79d6OuEhYUpPDxc\nkmRzq6T4+PjS2SGUKD8/P3rlIuiVa6FfroNeuY7y0CunX+hZ2sPd3d3s3r3b5Js5c2ah8/bu3WuM\nMWbHjh2mUqVKDs89+OCDJi8vz2RmZpoqVapc9zW5OcZ1BheFu86gV6416JfrDHrlOoObY8rAhAkT\n5Ofnp8mTJyshIUGhoaHq0qVLgXmnTp2SJH377bcF3o5OTExUUlKSatasKT8/vzKpGwAAoDyp8MEx\nMDBQgwcPVmJiooYPH66+ffsqJydHM2bMUO3atR3m7tu3T9L/BcgrnTx5UpJUrVq10i0aAACgHKrQ\nwdHT01PR0dHKzc1VSEiILly4oF27dmnUqFHy8vJy+OBvSVq5cqUk6f777y+wrapVq9r/akxycnKp\n1w4AAFDeVOjgOH36dHl7e2vkyJHasWOHfXlERITWrVunHj16qE+fPvblX3/9tVJTU9WrVy/7Hdb5\nRo0apVq1amn16tUOn/0IAABwM3H6hZ6lMUJCQowxxqxZs8a4ubkVeP7OO+80WVlZ5sSJE8bb29u+\n/KmnnjI5OTkmJyfHzJkzx0ycONGsW7fOGGPM0aNHTZMmTSy9PjfHuM7gonDXGfTKtQb9cp1Br1xn\ncHNMKfDx8dHUqVOVmZmpF198UcaYAnOSk5M1bNgweXp6Kioqyr585cqVCggI0LfffqunnnpKQ4YM\nUaNGjTRt2jQ1b95c+/fvL8tdAQAAKDcq5Oc4pqSkyNPT87rzIiMjFRkZWWB5YmKievToURqlAQAA\nuKwKecYRAAAAJY/gCAAAAEsIjgAAALCE4AgAAABLCI4AAACwhOAIAAAASwiOAAAAsITgWEounMtx\ndgkAAAAliuAIAAAASwiOAAAAsITgCAAAAEsIjgAAALCE4AgAAABLCI4AAACwhOAIAAAASwiOAAAA\nsITgCAAAAEsIjgAAALCE4AgAAABLCI4AAACwhOAIAAAASwiOAAAAsITgCAAAAEsIjgAAALDETZJx\ndhEVUVZWlvbt2+fsMmBBnTp1lJGR4ewyYAG9ci30y3XQK9dRWr1q1KiR6tWrZ2muYZT8iI+Pd3oN\nDHpV0Qa9cq1Bv1xn0CvXGc7uFW9VAwAAwBKCIwAAACyxSRrr7CIqqq1btzq7BFhEr1wHvXIt9Mt1\n0CvX4cxecXMMAAAALOGtagAAAFhCcLwBHTt21N69e/Xrr79q+PDhhc6ZMmWKfv31V23fvl3Nmzcv\n4wpxuev165577tGGDRuUk5Oj119/3QkVIt/1evXCCy9o+/btSkxM1Pr16/Xggw86oUpI1+/Vs88+\nq+3btyshIUHx8fFq3bq1E6pEPiv/bkmSv7+/cnNz9fzzz5dhdbjc9XrVtm1bnTp1SgkJCUpISNCo\nUaPKrDan31ruiqNSpUpm//795q677jJVqlQx27ZtM35+fg5zgoKCTGxsrJFkWrZsaTZt2uT0um/W\nYaVfdevWNf7+/mb8+PHm9ddfd3rNN+uw0qtWrVqZWrVqGUmmU6dO/GyV4155eHjYv37ggQfMnj17\nnF73zTqs9Ct/3qpVq8zSpUvN888/7/S6b8ZhpVdt27Y13377bdnXJhRLQECA9u/fr6SkJOXm5mre\nvHnq2rWrw5yuXbvqs88+kyRt3rxZtWrVkpeXlzPKvelZ6Vd6erp+/vln5ebmOqlKSNZ6tXHjRp06\ndUqStGnTJt1xxx3OKPWmZ6VXZ86csX/t4eEhY0xZl4n/z0q/JOlvf/ubvv76ax07dswJVUKy3itn\nIDgWk7e3t1JSUuyPDx06JG9v7yLPQdmgF66jqL0KDQ3Vd999Vxal4QpWe/Xcc89pz549Wrp0qfr3\n71+WJeIyVvp1++23q1u3bpo2bVpZl4fLWP3Zeuyxx7R9+3bFxsbq3nvvLZPaKpfJqwBAKXjyyScV\nGhqqNm3aOLsUXMPChQu1cOFCPf7443rnnXcUGBjo7JJwFZMnT9bw4cM5M+wCtm7dqoYNG+rMmTMK\nCgrSwoUL1bRp01J/XYJjMaWmpsrHx8f++I477lBqamqR56Bs0AvXYbVXDzzwgGbOnKmgoCCdOHGi\nLEvE/1fUn6sffvhBd999t2rXrq3jx4+XRYm4jJV++fv7a968eZL++JvInTt3Vl5enhYtWlSmtd7s\nrPTq9OnT9q+/++47/ec//ym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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d12f672780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Relative importance of the features: \",model.feature_importances_)\n",
    "with plt.style.context('dark_background'):\n",
    "    plt.figure(figsize=(10,7))\n",
    "    plt.grid(True)\n",
    "    plt.yticks(range(n_features+1,1,-1),df.columns[:-1],fontsize=20)\n",
    "    plt.xlabel(\"Relative (normalized) importance of parameters\",fontsize=15)\n",
    "    plt.ylabel(\"Features\\n\",fontsize=20)\n",
    "    plt.barh(range(n_features+1,1,-1),width=model.feature_importances_,height=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Print the $R^2$ score of the Random Forest regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 557,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Regression coefficient: 0.811794737752\n"
     ]
    }
   ],
   "source": [
    "print(\"Regression coefficient:\",model.score(X,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Benchmark to statsmodel (ordinary least-square solution by exact analytic method)\n",
    "\n",
    "[Statsmodel is a Python module](http://www.statsmodels.org/dev/index.html) that provides classes and functions for the estimation of many different statistical models, as well as for conducting statistical tests, and statistical data exploration. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 558,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 559,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xs=sm.add_constant(X)\n",
    "stat_model = sm.OLS(y,Xs)\n",
    "stat_result = stat_model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 560,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.971\n",
      "Model:                            OLS   Adj. R-squared:                  0.969\n",
      "Method:                 Least Squares   F-statistic:                     521.4\n",
      "Date:                Thu, 04 Jan 2018   Prob (F-statistic):           2.79e-69\n",
      "Time:                        23:56:18   Log-Likelihood:                -434.92\n",
      "No. Observations:                 100   AIC:                             883.8\n",
      "Df Residuals:                      93   BIC:                             902.1\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.9153      2.056      0.445      0.657      -3.167       4.998\n",
      "x1            38.2702      1.900     20.142      0.000      34.497      42.043\n",
      "x2            69.6705      1.888     36.908      0.000      65.922      73.419\n",
      "x3            75.1667      2.057     36.546      0.000      71.082      79.251\n",
      "x4            -0.3881      2.073     -0.187      0.852      -4.505       3.729\n",
      "x5            -1.3036      2.038     -0.640      0.524      -5.352       2.744\n",
      "x6            -0.2271      2.112     -0.108      0.915      -4.420       3.966\n",
      "==============================================================================\n",
      "Omnibus:                        0.366   Durbin-Watson:                   1.855\n",
      "Prob(Omnibus):                  0.833   Jarque-Bera (JB):                0.531\n",
      "Skew:                           0.044   Prob(JB):                        0.767\n",
      "Kurtosis:                       2.654   Cond. No.                         1.47\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(stat_result.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Make arrays of regression coefficients estimated by the models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 561,
   "metadata": {},
   "outputs": [],
   "source": [
    "rf_coef=np.array(coef)\n",
    "stat_coef=np.array(stat_result.params[1:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Show the true regression coefficients (as returned by the generator function) and the OLS model's estimated coefficients side by side"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 562,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th>X4</th>\n",
       "      <th>X5</th>\n",
       "      <th>X6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>True Regressors</th>\n",
       "      <td>38.474632</td>\n",
       "      <td>71.735567</td>\n",
       "      <td>72.595476</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OLS method estimation</th>\n",
       "      <td>38.270216</td>\n",
       "      <td>69.670541</td>\n",
       "      <td>75.166745</td>\n",
       "      <td>-0.388141</td>\n",
       "      <td>-1.303634</td>\n",
       "      <td>-0.227058</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              X1         X2         X3        X4        X5  \\\n",
       "True Regressors        38.474632  71.735567  72.595476  0.000000  0.000000   \n",
       "OLS method estimation  38.270216  69.670541  75.166745 -0.388141 -1.303634   \n",
       "\n",
       "                             X6  \n",
       "True Regressors        0.000000  \n",
       "OLS method estimation -0.227058  "
      ]
     },
     "execution_count": 562,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_coef = pd.DataFrame(data=[rf_coef,stat_coef],columns=df.columns[:-1],index=['True Regressors', 'OLS method estimation'])\n",
    "df_coef"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show the relative importance of regressors side by side\n",
    "\n",
    "For Random Forest Model, show the relative importance of features as determined by the meta-estimator. For the OLS model, show normalized t-statistic values.\n",
    "\n",
    "**It will be clear that although the RandomForest regressor identifies the important regressors correctly, it does not assign the same level of relative importance to them as done by OLS method t-statistic**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 563,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th>X4</th>\n",
       "      <th>X5</th>\n",
       "      <th>X6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>RF Regressor relative importance</th>\n",
       "      <td>0.034562</td>\n",
       "      <td>0.469594</td>\n",
       "      <td>0.495001</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OLS method normalized t-statistic</th>\n",
       "      <td>0.217370</td>\n",
       "      <td>0.398305</td>\n",
       "      <td>0.394407</td>\n",
       "      <td>-0.00202</td>\n",
       "      <td>-0.006902</td>\n",
       "      <td>-0.001160</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                         X1        X2        X3       X4  \\\n",
       "RF Regressor relative importance   0.034562  0.469594  0.495001  0.00000   \n",
       "OLS method normalized t-statistic  0.217370  0.398305  0.394407 -0.00202   \n",
       "\n",
       "                                         X5        X6  \n",
       "RF Regressor relative importance   0.000000  0.000843  \n",
       "OLS method normalized t-statistic -0.006902 -0.001160  "
      ]
     },
     "execution_count": 563,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_importance = pd.DataFrame(data=[model.feature_importances_,stat_result.tvalues[1:]/sum(stat_result.tvalues[1:])],\n",
    "                             columns=df.columns[:-1],\n",
    "                             index=['RF Regressor relative importance', 'OLS method normalized t-statistic'])\n",
    "df_importance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further explorations\n",
    "\n",
    "Play with the hyperparameters of the models e.g. tree depth, leaf quantity, splitting strategy, number of trees in the forest, etc. to see how the regression model behaves. Also, play with the nature and complexity of the sample generator by writing your own nonlinear function."
   ]
  }
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